The Golden Section Search Method: Modifying the Bisection Method with the Golden Ratio for Numerical Optimization

Introduction

The first algorithm that I learned for root-finding in my undergraduate numerical analysis class (MACM 316 at Simon Fraser University) was the bisection method. It’s very intuitive and easy to implement in any programming language (I was using MATLAB at the time). The bisection method can be easily adapted for optimizing 1-dimensional functions with a slight but intuitive modification. As there are numerous books and web sites on the bisection method, I will not dwell on it in my blog post.

Instead, I will explain a clever and elegant way to modify the bisection method with the golden ratio that results in faster computation; I learned this method while reading “A First Course in Statistical Programming with R” by John Braun and Duncan Murdoch. Using a script in R to implement this special algorithm, I will illustrate how to minimize a non-differentiable function with the…